Ray Allen (UFA)

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One question looms over Ray Allen after a forgettable 2011-12 season with the Celtics: Is the 36-year-old shooting guard hurt, washed up, or both?

You don’t need to spend long combing the numbers to know something was amiss. He averaged the fewest points (14.2) and minutes (34.0) since his rookie season and posted career lows in rebounds (3.1) and assists (2.1).

However, his three-point shooting held at an impressive 45.3 percent, meaning he may still be the starting two the Bulls have sought since Ben Gordon departed.

If the Bulls opt to go cheap on a point guard and spend the Mid-Level to bolster the wing, Allen is as good an option as any available.

Jerryd Bayless (RFA)

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Coming into the NBA, Jerryd Bayless was billed as a dynamic talent who could play either guard position. And while he's only seen big minutes in Toronto when Jose Calderon has been injured, he looked strong in his starts this season, averaging 17.8 points and 5.3 assists.

Bayless isn’t a prototypical "1", but the Bulls are built to rely on scoring from the point guard position. Furthermore, he could be a nice option at shooting guard once Rose comes back, or a strong sixth man off the bench.

If the Bulls hear that Toronto is willing to let Bayless walk, signing him to an offer sheet would be a worthwhile gamble.

Andre Miller (UFA)

That’s exactly what the Bulls can offer him for most of the 2012-13 season.

In seven starts this season, the 36-year-old veteran averaged 14.0 PPG and 10.1 assists. And while he doesn’t have the speed to run the open court, he keyed the Nuggets’ transition game by grabbing rebounds and throwing timely outlet passes.

Miller isn’t a player who can lead the Bulls out of the first round of the playoffs, but he can be productive enough in the regular season to make sure they get there.

Aaron Brooks (RFA)

Just two seasons ago, Aaron Brooks averaged 19.6 PPG with a 54.9 True Shooting (TS) percentage as an 82 game starter for the Houston Rockets.

By comparison, Rose has topped that level of efficiency just once in his career, and only by slimmest of margins: He hit for 55.0 percent TS in 2010-11, his MVP season.

While it goes without saying that Rose is the better scorer, Brooks is capable of having big games himself: he scored at least 30 points in 10 games in 2009-10, including a season high 43 points against the Minnesota Timberwolves.

That’s the kind of explosiveness the Bulls will need if they want to be competitive in 2012-13.